SRINAGAR, India — Separatist leaders called for a shutdown in Indian-controlled Kashmir on Saturday as Indian Prime Minister Narendra Modi paid a daylong visit to review development work and inaugurate road projects.

The visit came a day after rivals India and Pakistan shelled each other’s security posts and villages, killing four civilians on each side and an Indian soldier.

Shops, businesses and schools were shut while thousands of paramilitary troops and police in flak jackets spread out across Kashmir and closed off roads with razor wire and iron barricades in anticipation of anti-India protests and clashes.

Separatist groups that challenge India’s sovereignty over Kashmir called for the strike as well as a march to the commercial hub in the main city of Srinagar to protest Mr. Modi’s visit.

Government forces implemented a security lockdown in downtown Srinagar, the urban heart of anti-India protests, as they warned residents to stay home.

Road traffic was sparse, with buses staying off the roads and few cars venturing out.

Authorities detained dozens of activists overnight and put separatist leaders under house arrest to stop them from staging the protest march. They also ordered schools and colleges to be closed for the day.

Mr. Modi arrived in the remote mountainous Ladakh region bordering China and Pakistan, where he inaugurated work on a strategic tunnel connecting the cold desert region with the Kashmir Valley.

Later in Srinagar, Mr. Modi inaugurated, remotely, a controversial hydroelectric power project built in the Gurez Valley, just a few hundred yards from the highly militarized Line of Control that divides Kashmir between India and Pakistan. He dedicated the power station to the nation at a lakeside venue.

“Every stone, every weapon picked up by misguided youths destabilizes their own Jammu-Kashmir,” Mr. Modi said in his speech, referring to anti-India protesters. “Every issue, every problem has one solution: development, development and development.”

Pakistan has objected to the design of the power project, invoking the Indus Water Treaty. The neighboring countries signed the treaty in 1960 to share the vast water resources from the Indus River system, which supplies water to both.

On Friday, Pakistan expressed serious concerns over the project, with the Foreign Ministry saying in a statement that “the inauguration of the project without the resolution of the dispute is tantamount to violation of the Indus Waters Treaty.”

India has said in the past the project’s design is within the parameters of the treaty.

India and Pakistan each administer part of Kashmir, but both claim it in its entirety. Rebels have been fighting Indian rule since 1989, demanding Indian-controlled Kashmir be united either under Pakistani rule or as an independent country.